RESIDUAL STRESS AND DEFORMATION INDUCED BY LASER SHOCK
PEENING ON TITANIUM ALLOYS
a
C. Cellard a, P. Osmond a, D. Retraint a, E. Rouhaud a, S. Rémy a and A. Viguera-Sancho b
Université de Technologie de Troyes (UTT), 12 Rue Marie Curie BP 2060 10010 TROYES Cedex
b
SNECMA Evry – Corbeil, Route Henry Auguste Desbruères BP 81 91003 EVRY Cedex
ABSTRACT
An investigation on residual stresses and deformations induced by laser shock peening on titanium alloys was undertaken.
The samples were provided by SNECMA and are representative of the titanium alloys used in the aeronautic field: Ti-6Al-4V
(TA6V) and Ti-5Al-2Sn-2Zr-4Cr-4Mo (Ti-17). The specimens were laser shocked with modifications of different parameters
(laser fluence, pulse duration and number of laser impacts) in order to obtain various compression depths: 0.5 - 1 - 1.5 –
3 mm. The residual stress profiles were obtained by two methods: X-Ray diffraction and crack compliance method. The
deformations induced by laser shock peening were established experimentally by the determination of the global shape of the
samples with two processes: laser triangulation and a coordinate measuring machine. From the knowledge of the residual
stress profile, it is possible to get numerically the global shape of the specimens which is then compared with those obtained
experimentally. A good agreement is obtained.
1.
Introduction
While flying, a turbojet can swallow different foreign objects (birds, fragments, etc.). Damage induced by these objects is
known as FOD (Foreign Object Damage), and can lead to the cracking of fan blades. In order to reduce maintenance costs,
engine manufacturers try to find a way to increase the fatigue life, after FOD, of fan blades by introducing compressive residual
stresses. Various surface treatments and modification technologies have been developed to induce a protective layer so as to
increase the fatigue life. One of them, shot peening, is well established and routinely applied in aeronautics. However, this
technology has a number of limitations: the depth of the compressive residual stresses is relatively small (about 0,2 mm), the
plastic strains are important and the material is work-hardened. This can lead to damage of the material microstructure and
accelerate the relaxation of the residual stresses.
The application of laser shock peening could overcome these drawbacks [1]. Developed in the beginning of the 70’s, this
treatment introduces, compared to shot peening, high compressive residual stresses but deeper into the part with very small
work hardening observed, leading to an appreciable increase of fatigue life. The objective of the present study is to measure
the residual stress profiles obtained along with an evaluation of the global deformation that is generated on the part to evaluate
the possible applications in aeronautics.
Figure 1: Laser shock peening process [1]
2.
Description of the experimental protocol
2.1. Laser shot peening
The principle of laser shot peening is presented in Figure 1. It is based on the use of a laser pulse, which duration is of the
order of a few nanoseconds with a fluence range from 1 to 10 GW/cm², to generate a plasma by vaporizing a thin opaque layer
(or coating layer). The expansion of the plasma generates shock waves that propagate into the material due to the confining
medium. The shock waves, by penetrating into the material, plastically deform the body in order to introduce compressive
residual stresses in depth.
The present investigation brings out the residual stresses and deformations induced by laser shock peening on titanium alloys.
The residual stress profiles were evaluated with different methods (X-Ray diffraction and crack compliance method) to get a
good precision on the surface of the specimen as well as in depth. The deformations were established experimentally, by laser
triangulation and a coordinate measuring machine (CMM).
The dimensions of the laser shocked samples are: 50 x 50 x 12.5 mm. They were laser shocked with the same parameters to
introduce compressive stresses till 3mm depth.
2.2. Experimental determination of the residual stress profile
2.2.1. X-Ray diffraction
X-Ray diffraction enables to investigate on the residual stresses in a region near the surface (in the order of 5µm) [2]. It is
based on the sin² ψ relation [3], when σ33 = 0:
æ 1 ö
æ 1
÷÷ s 11f sin ²y + s 13f sin 2y + çç
2q fy = 2q 0 + çç
è K 1 ø hkl
è K2
[
where
]
ö
f
÷÷ s 11f + s 22
ø hkl
[
]
(1)
æ 1 ö
360
æ1 ö
çç
÷÷ = tan q 0 ç S 2 ÷ in MPa -1
p
è 2 ø hkl
è K 1 ø hkl
(2)
æ 1
çç
è K2
(3)
ö
360
÷÷ = tan q 0 (S 1 )hkl in MPa -1
p
ø hkl
((1/2)S2)hkl and (S1)hkl = X-ray elasticity constants (XEC)
θ0 = value of θ (Bragg’s angle) when the body is stress free
The XEC are either determined experimentally, either calculated from the constants of the single crystal taking into account the
coupling between crystallites and the surrounding matrix. In our case they are taken from the literature [4]:
S1 = -2.64*10-6 MPa-1
(1/2)S2 = 11.90*10-6 MPa-1
In this way, to evaluate the macroscopic stress state the sin²ψ graph is plotted, by varying the angle ψ during the
measurement of dhkl, to get the stresses in direction Φ. We obtain:
A line in case of biaxial stress state (<σ13>=0)
An ellipse in case of triaxial stress state
The use of X-Ray diffractometer leads us to choose several parameters. The intensity and voltage applied to the X-ray tube,
as well as the acquisition time, will influence the counting statistics of the diffraction patterns. A compromise has to be found
between acquisition time and quality of the diffractogram.
The parameters used are the followings:
Copper anode tube (λ = 0,154mm)
Voltage: 40 kV
Intensity: 30 mA
Acquisition time: 420s
The diffraction peaks: family planes, value of the angles 2θ and ψ were chosen as follow:
Plane family {211}
Acquisition range 2θ: [105 ; 117]°
ψ values: {-60°, -52.23°, -45°, -37.76°, -30°, -20.7°, 0°, 10°, 25°, 34°, 42°, 49° and 56°}
2.2.2. Crack Compliance Method
The idea of the method is to continuously introduce a cut in the body. The deformation induced by the relaxation of the
stresses is measured and a calculation determines the residual stresses in the cut region. The main advantages of the method
are the capability to determine the residual-stress distribution on the entire cross-section of a structural part by only one or a
few strain-gages, and to deliver the residual stresses in a form well-suited for their use in stress engineering, including the
stress intensity factor acting on cracks. The main disadvantage is its nature as a destructive method, since it requires a cut
along the considered cross-section. The method is practically restricted to 2D structures, because the determination of the
general relaxation behaviour of an elastic body in 3D due to a cut is rather complex from a mathematical point of view.
A cut has to be introduced along the plane where the residual stresses are to be determined, as shown in Figure 2 [5] for the
case of a rectangular plate with a cut along its central section. If the cut is relatively narrow (d<<a and d<<(W-a)), it can be
regarded as a crack. So, the basic equations of linear elastic fracture mechanics can be used to establish the required
mathematical relation between the residual stress and the strain change at the measurement point.
y
d
a
W
M
x
Figure 2: Rectangular plate, cut along its centre plane; strain measurement at point M
The Stress Intensity Factor at the tip of the cut due to residual stress is given by [6]:
K Irs (a ) =
where
E ' de M
Z (a ) da
(4)
εM = strain measured at the arbitrary point M
E’ = generalized Young’s modulus
Z(a) = “influence function”
εM is measured during the cutting process and recorded as a function of the cut depth a.
E’ = E for plane stress and E’=E/(1-υ²) for plane strain.
Z(a) is a unique function that depends on the component geometry, on the cut plane and on the location of the measurement
point M, but not on the residual stress distribution. It characterizes the sensitivity of the measurement point M with respect to
the stress released at the cut plane. Determination of Z(a) is crucial and the most demanding step of the CC-method.
However, Z(a) needs to be determined only once for a certain geometry and measurement point.
Klrs(a) results from the normal residual stresses acting prior to cutting, σrs(x) (the x axis being chosen such that it coincides with
the crack line, or cut plane, respectively), by the general relation [6]:
a
K Irs (a ) = ò h( x, a ).s rs ( x).dx
(5)
0
where
h(x,a) = weight function
The weight function is universal for a given crack geometry and available for many systems. σrs(x) can be obtained by
inversion of equation 5.
2.2.3. Experimental residual stress profiles
The residual stress profiles have been determined and compared with two specimens as presented on Figure 3.
Figure 3: Comparative of results: X-Ray diffraction and crack compliance for Ti-17 and TA6V samples (3 mm compression)
The values of the residual stresses in surface, obtained with X-Ray diffraction, seem coherent with the residual stress profile
established by the crack compliance method. Even if the disparity, in term of value, is important between the point in surface
and the first point in depth (100µm), it remains representative of a laser shocked residual stress profile.
Furthermore, we can notice that the compressive stresses are deep (the profile cancels at a depth > 1 mm).
2.3. Experimental determination of the deformations induced by laser shock peening
A high link exists between stresses and residual deformations. Some investigations have been carried out in order to link
together deformations and residual stresses on simple geometries [7]. So, sufficient precise methods have been finalized to
determine the shape of the residual stress profile from the knowledge of mechanic and geometric quantities. However, these
methods are not applicable to complex geometries because of the difficulty to evaluate geometric quantities.
2.3.1. Determination of the global shape with a coordinate measuring machine (CMM)
The samples were sensored in their “piece reference” defined in the Figure 4:
The plane XY is defined from 3 points on the treated surface
The direction X is determined by scanning two points on the front face
The direction Y is determined by scanning the lateral face
Lateral face
Sensor line at
constant y
Sensor line at
constant x
Front face
Figure 4: Definition of the piece reference and measurement square pattern
The square pattern is 21 x 21 points and the increment between each point is 2.25 mm, allowing a geometric data acquisition
on the whole piece while avoiding the possible sensor aberrations near the edge of the piece. In total, 441 points have been
sensored. In order to minimize the influence of the laser spot, a high diameter sphere (6 mm) is used as sensor.
Deformation (mm)
The processing of geometric data is simple. In fact, with the sensor, the global shape of the samples is directly measured
(Figure 5), it only remains to deduce the curvature for the two sensor lines at constant x and constant y.
Global shape measured at y constant
x (mm)
Figure 5: Global shape measured at y constant on TA6V sample (3mm compression)
Even if the sensor sphere has an important diameter (6 mm), some noise is perceptible due to laser spot.
The method used to evaluate the curvature is the polynomial regression. In order to ensure a good correlation, the degree of
the polynomial is fixed between 3 and 6. Once the function determined, the curvature is calculated with the following
expression:
1
1
(6)
R
where
=
3
(1 + f '²) 2
f ''
R = curvature radius
f = polynomial function
This method gives a good quality of the results in the central part of the signal. However, we have to be cagey about the
values obtained at the two extremities because the polynomial is in “adaptation period” (Figure 6), which can induce errors.
Adaptation period of
the polynomial
Figure 6: Polynomial regression; global shape get on TA6V sample (3 mm compression)
2.3.2. Determination of the global shape with laser triangulation and comparison
The sensor employed is a CCD displacement sensor of high precision. The CCD displacement indicator, laser Keyence LK031, is based on the measurement by laser triangulation: a semi-conductor laser beam is reflected by the surface of the
material and goes through a system of lens. The beam concentrates on a CCD detection matrix. The CCD detects the peak
value of the distribution of the light quantity of the beam spot. The CCD pixels of the beam spot are used to determine the
precise position of the target. The sensor emits a 670 nm wave length red visible beam. The spot diameter is 30 µm and has a
resolution of 1 µm. The laser sensor has a linearity of ±0,1% of full scale and an ideal work distance of 30±5 mm from the
sample. The laser sensor is connected to an acquisition machine, allowing the collection of geometric data similar to the
previous process but in higher number. For each sample, 4 directions are sensored: horizontal, vertical and the two diagonals
of the sample. The data analysis showed that the profiles were shifted. In order to redress them, two successive interpolations
were carried out: first with a polynomial of degree 2 and second, with a polynomial of degree 1. Finally, a polynomial
regression is performed to determine the curvature.
Deformation (mm)
The global shapes obtained with laser triangulation and a coordinate measuring machine are then compared as shown in
Figure 7.
CMM
Laser triangulation
Position (mm)
Figure 7: Comparisons of the global shapes of Ti-17 sample (3 mm compression) obtained with laser triangulation and CMM
We can notice that the deformations induced by laser shock peening are small (amplitude of the global shape is nearly 16 µm
taking into account that the thickness of the sample is 12.5 mm).
3.
Numerical determination of the deformations
The calculation of the curvature of the sample is possible if the residual stress profile is known when the sample is not
constrained. We can then calculate the plastic deformation associated to this profile with the following relation [7]:
1 -u
s - (A z + B) = e p
E
(7)
Where A and B are constants relative to the curvature and the elongation of the specimen respectively.
From the expression of εp we can deduce the stress profile when the sample is constrained with the relation [7]:
s constrained = e p .
E
1 -u
(8)
This profile is then introduced in the Finite Element software Zset [8] to determine the global shape when the sample is not
constrained. The calculation is elastic and realised in two steps:
Introduction of the residual stress profile when the specimen is constrained.
Relaxation of the boundary conditions and elastic readjustment of the specimen.
Only one quarter of the specimen is modelled with adequate symmetry conditions applied to limit computation time. The
boundary conditions applied are the followings (Figure 8):
On the first step, the faces 1, 2 and 3 have no displacement according to x, y and z respectively.
On the second step, the faces 1, 2 and 3 are free.
Face 4
Face 5
Face 2
Face 3
Face 1
Figure 8. Boundary conditions
The material behaviour is linear elastic:
Young modulus: 117000 MPa
Poisson’s ratio: 0,33
The introduction of the residual stresses is realised in two steps:
From the experimental values by X-Ray diffraction and crack compliance, a polynomial regression gives the residual
stress profile when the sample is constrained. The plastic depth is 3,81 mm.
The knowledge of the residual stresses enables to determine (with relation 8) the associated plastic deformation.
The elements are c3d20: 20 nodes hexaedric continuous element (quadratic). They are extruded from a 2D mesh and their
thickness is variable: fine mesh on the upper face to get a good precision and coarse when we move away. This operation
reduces the calculation time while the good quality of the results is maintained.
4.
Comparison numerical / experimental global shape
Figure 9 shows the comparison between the numerical and experimental global shape, by the coordinate measuring machine,
of the Ti17 (3mm compression) sample:
Figure 9. Comparison of the numerical and experimental global shape of the specimen
We observe a good correlation between the numerical and experimental values of the global shape. This confrontation allows
us to correlate the experimental residual stress profile, and validate the method to introduce residual stresses in a Finite
Element Model as well as the calculation of the curvature.
5.
Conclusions
This study presents the deformations and the residual stresses induced by laser shot peening on titanium alloys. The
determination of the residual stress profiles shows that the maximal compressive stress is located near the surface and its
value is high (approximately -1100 MPa). Furthermore, the compressive stresses are deep (the profile cancels at a depth
> 1 mm). However, the deformations induced by laser shock peening are small (amplitude of the global shape nearly 16 µm
taking into account that the depth of the sample is 12.5 mm), which is one of the principal advantages of this method because
it offers a good integrity of the surface and improves the fatigue life.
The experimental determinations, by different methods, of the global shape and residual stress profiles show a good
correlation. It is the same for the comparison of the numerical and experimental global shapes which allows us to validate the
residual stress profile established experimentally by X-Ray diffraction and crack compliance.
Acknowledgements
The present study was financed by SNECMA (Safran group). Some methodologies and results were extracted from internal
reports.
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